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Simplifying 7x + -3 = -5 + 6x(4x + 3) Reorder the terms: -3 + 7x = -5 + 6x(4x + 3) Reorder the terms: -3 + 7x = -5 + 6x(3 + 4x) -3 + 7x = -5 + (3 * 6x + 4x * 6x) -3 + 7x = -5 + (18x + 24x2) Solving -3 + 7x = -5 + 18x + 24x2 Solving for variable 'x'. Reorder the terms: -3 + 5 + 7x + -18x + -24x2 = -5 + 18x + 24x2 + 5 + -18x + -24x2 Combine like terms: -3 + 5 = 2 2 + 7x + -18x + -24x2 = -5 + 18x + 24x2 + 5 + -18x + -24x2 Combine like terms: 7x + -18x = -11x 2 + -11x + -24x2 = -5 + 18x + 24x2 + 5 + -18x + -24x2 Reorder the terms: 2 + -11x + -24x2 = -5 + 5 + 18x + -18x + 24x2 + -24x2 Combine like terms: -5 + 5 = 0 2 + -11x + -24x2 = 0 + 18x + -18x + 24x2 + -24x2 2 + -11x + -24x2 = 18x + -18x + 24x2 + -24x2 Combine like terms: 18x + -18x = 0 2 + -11x + -24x2 = 0 + 24x2 + -24x2 2 + -11x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 2 + -11x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -0.08333333333 + 0.4583333333x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.4583333333x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.4583333333x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.4583333333x + x2 = 0 + 0.08333333333 0.4583333333x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.4583333333x + x2 = 0.08333333333 The x term is 0.4583333333x. Take half its coefficient (0.2291666667). Square it (0.05251736113) and add it to both sides. Add '0.05251736113' to each side of the equation. 0.4583333333x + 0.05251736113 + x2 = 0.08333333333 + 0.05251736113 Reorder the terms: 0.05251736113 + 0.4583333333x + x2 = 0.08333333333 + 0.05251736113 Combine like terms: 0.08333333333 + 0.05251736113 = 0.13585069446 0.05251736113 + 0.4583333333x + x2 = 0.13585069446 Factor a perfect square on the left side: (x + 0.2291666667)(x + 0.2291666667) = 0.13585069446 Calculate the square root of the right side: 0.368579292 Break this problem into two subproblems by setting (x + 0.2291666667) equal to 0.368579292 and -0.368579292.Subproblem 1
x + 0.2291666667 = 0.368579292 Simplifying x + 0.2291666667 = 0.368579292 Reorder the terms: 0.2291666667 + x = 0.368579292 Solving 0.2291666667 + x = 0.368579292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2291666667' to each side of the equation. 0.2291666667 + -0.2291666667 + x = 0.368579292 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = 0.368579292 + -0.2291666667 x = 0.368579292 + -0.2291666667 Combine like terms: 0.368579292 + -0.2291666667 = 0.1394126253 x = 0.1394126253 Simplifying x = 0.1394126253Subproblem 2
x + 0.2291666667 = -0.368579292 Simplifying x + 0.2291666667 = -0.368579292 Reorder the terms: 0.2291666667 + x = -0.368579292 Solving 0.2291666667 + x = -0.368579292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2291666667' to each side of the equation. 0.2291666667 + -0.2291666667 + x = -0.368579292 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = -0.368579292 + -0.2291666667 x = -0.368579292 + -0.2291666667 Combine like terms: -0.368579292 + -0.2291666667 = -0.5977459587 x = -0.5977459587 Simplifying x = -0.5977459587Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1394126253, -0.5977459587}
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